If the image was already published, and the activation time is in the future, SPS shows it as unpublished.

If the image was unpublished already, mark it as published. SPS shows it as unpublished if the activation is in the future.

When I view the Last Published field for my asset in the detail view of SPS, it lists my asset as not published. Why is that?

The publish flag is not set.

If you are using Image Rendering, compare the upload or last modified time stamps for the asset to the time stamp of the last relevant publish. If the asset was uploaded or marked for publish after the last publish began, it would not have been included in the publish list. Make sure that the asset is marked for publish, and then run the IR publish job.

The asset is a non-Image Serving asset. The "Last Published" field uses a req=exists request to check for the asset's availability on the Image Servers. This request type is not supported for Image Rendering at this time, so IR assets, such as Vignettes and Material images, are always listed as Not Published, regardless of whether the asset is published.

The server name listed under SPS Setup isn't the correct host name for the servers your assets publish to. Contact Tech Support for assistance.